# Predict then Propagate: Graph Neural Networks meet Personalized PageRank

arXiv: https://arxiv.org/abs/1810.05997 · HTML: https://mlsanity.com/paper/1810.05997/

## Key facts

- Cited by 993 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2018.

## Built on by (most cited first, 30 of 993)

- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction](https://mlsanity.com/paper/2111.00064/) (2021)
- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations](https://mlsanity.com/paper/2306.10759/) (2023)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [Learning Graph Embeddings for Compositional Zero-shot Learning](https://mlsanity.com/paper/2102.01987/) (2021)
- [GraphText: Graph Reasoning in Text Space](https://mlsanity.com/paper/2310.01089/) (2023)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [GNNAutoScale: Scalable and Expressive Graph Neural Networks via Historical Embeddings](https://mlsanity.com/paper/2106.05609/) (2021)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)

## Abstract (arXiv)

Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of this utilized neighborhood is hard to extend. In this paper, we use the relationship between graph convolutional networks (GCN) and PageRank to derive an improved propagation scheme based on personalized PageRank. We utilize this propagation procedure to construct a simple model, personalized propagation of neural predictions (PPNP), and its fast approximation, APPNP. Our model's training time is on par or faster and its number of parameters on par or lower than previous models. It leverages a large, adjustable neighborhood for classification and can be easily combined with any neural network. We show that this model outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. Our implementation is available online.